Heretofore, studies on the scanning line density conversion systems have been conducted in the field of the international television transmission system, primarily centered on the system composed of a camera and a picture monitor and the line interpolation system. The former system is less costly, with such a demerit of picture deterioration as non-linear distortions, and the latter system has a defect of involving complicated processing. In facsimile communication, since its conversion system, as far as its application field and condition are concerned, is different from that for a television system in respect that as the signal is obtained in the form of hard copy, while a high degree of real time nature is not required, the effect of its conversion distortion tends to stand out. In respect to the scanning line density conversion of facsimile signal, such systems as OPC (ordinal processing conversion) and SPC (selective processing conversion) were proposed (See: The 7th National Convention of the Institute of Image Electronics Engineers of Japan, Collection of scripts, script No. 10, May 19, 1975). These systems are either to successively read out the picture elements of an original picture for successively replacing the picture elements of the converted output picture by the original picture, or to replace the pictue elements of the output picture by the nearest picture elements of the original picture. As the effect of distortion on the picture due to the conversion of the scanning line density fluctuates in accordance with the relative position between the picture elements of the output picture and those of the original picture, they tend to undergo a deterioration in the quality of the picture such that the contour of an output picture become inordinately large.